In chapter 9 of the NKS book, Wolfram explains his conjectures about fundamental physics. He does not think QM is the bottom level description of our universe. He expects to find a computational network system from which the facts known to QM emerge as larger scale approximations. In traditional terms, he expects a "hidden variables" theory to be successful. If he is right, the universe will be found to be Turing computable.

Naturally, since he has only sketched his ideas on the subject and has not yet found such a theory, this remains speculative. I've heard from others(e.g. David Deutsch) the speculation that the universe is a computational system but as a quantum computer rather than a classical computer. Someone else might want to keep NKS methods for larger scale phenomena but not agree with either position as to the likely future of fundamental physics.

All seem to me reasonable positions to hold and fully compatible with NKS more broadly speaking. But Wolfram himself definitely takes the first of them, and expects a rigorously computable ultimate theory. This is sometimes referred to as the strong form of Church's thesis - that all processes physically realizable in our universe are (Turing) computable.

The book suggests that if we have a sufficiently powerful computer, we can run a complex automata, which will emulate behavour of our universe.

That is correct. If we knew precisely how the laws of physics work, we should be able to run a simulation of a universe running under the same laws of physics. It would be smaller than our own universe, due to the fact that a simulation cannot contain more information than the computer simulating it, but it could still be large enough to run a good portion of our universe. In fact, it is conceivable that intelligent life could arise in such a simulation, leading to a sort of Matrix scenario. This idea is described in detail here.

It is also possible for computers to run simulations of universes running under other sets of physical laws. In fact, every cellular automaton and probably every other program as well could be considered as being a simulated universe.

My question is:
How is it possible to run universe simulation, which is quantum, on a classical computer?

The idea is that the effects we see as being random are not actually random, but rather the result of nonrandom processes that are simply occuring on too small of a scale for us to detect them yet (and it's possible we will never be able to detect them). For example, imagine if you were running a cellular automaton of rule 110, only when you had a neighborhood of 101, rather than the result being 1, it was equal to the cell of a rule 30 cellular automaton running 'underneath' it. In the rule 110 universe, this would appear to be quite random, even though no randomness was actually involved. The idea is that something along these lines, nonrandom generation that appears random, is the basis of quantum 'randomness'.

Originally posted by green_meklar
The idea is that the effects we see as being random are not actually random, but rather the result of nonrandom processes that are simply occuring on too small of a scale for us to detect them yet...

I was refering to simulation of quantum physics, and i dont think simulation of classical random processes has anything to do with it.

Originally posted by Jason Cawley
[B]In chapter 9 of the NKS book, Wolfram explains his conjectures about fundamental physics. He does not think QM is the bottom level description of our universe. He expects to find a computational network system from which the facts known to QM emerge as larger scale approximations. In traditional terms, he expects a "hidden variables" theory to be successful. If he is right, the universe will be found to be Turing computable. ...

Hmm, but i dont think it really matters if its basic or not. We can clearly observe its effects, and classical computation is not able to do it* since at the basic level it requires the system to be able to register both 0 and 1 (or whatever basic bits the system is using) simultaneously.

As far as i undersand, NKS functions purely as a classical computation system. Hence it can not mimic quantum behavour.

This is my reason for NKS not being able to simulate the universe, since universe is clearly a quantum comutational system (doesnt matter wheather its basic level or not).

Sorry for my english, but i hope this is expressed in understandable form.

*I did a little research into this and in fact a classical computational system CAN simulate quantum system. This is done by mimicing quantum bit with a number of classical bits. As far as i understand, it is possible to completely mimic (i.e. establish isomorphism) quantum system via classical using this method. The only problem is that it takes exponentially more time with increased number of bits, required to describe the system. So basically for any but the most basic system and only for a very short time, the answer is that it practically cant.

"...smaller than our own universe, due to the fact that a simulation cannot contain more information than the computer simulating it"

Oh?

The best part about any system is it's boundary conditions...
On my table is a rock, does this rock have a system?
if so what does this system describe about this rock?
And how complete is the system in terms of defining the full scope of the rock?

Does it describe physical traits about the rock?
it's density?
the molecular arrangement?
does the system locate different regions of density and different arrangements of molecular structure?
does the system describe properties of physical entities such as the electrical energy of the rock?
does the system account for the vibrations of the molecules within the rock at its current temperature?

What exactly will a system want to describe?
And where are these boundary conditions located for my rock?
It’s my “Free” choice it seems to pick one, or some…

there is such a plethora of boundary systems of different types within my rock that a mathematical description of the entirety of this rock would look nothing as the rock it self..
I think it would be unjust to try to wrap the rock up within descriptions..
unless of course..
I needed something from my measurements that I could use to my advantage.

But then,
If all my measurements against my rock are about what I can extract from it then how much about it , if any, do I ignore within my approach?
Are my desires for handling this rock full enough to describe the full scope of this "system"...
Or will I unavoidably isolate out so that I may proceed forward…

What aspect am I after?

Then, if I take what I have seen within this rock and speak to another about what I now know, then in what form of reason do I give another what I have witnessed? If my description contains all elements of the rock then is my intelligence rewarded?
If my description ignores large portions about this rock then do I justify my intelligence?
And does that justification uphold my original intent to handle the rock in a way that is respectable?

And if I give my systems creation over to a computer..
Does my knowledge of the workings of this computer give me the ability to see the rock in the same light that the computer will describe?
And If the computer performs computations that I cannot fathom then how much should I trust this computer to describe the system in it’s entirety, to what degree of accuracy are my measurements compared to..

And if no comparison exists for my observations, then how will I catch what would be over looked..

Or can I be assured that I know all possible emanations that may manifest from this rock, therefore I need but be on the look out for the correct ones.

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A great revolution is at hand, but this is just a metaphor.